An Approach to Higher Dimensional Theories Based on Lattice Gauge Theory

TL;DR

This paper explores a novel approach to higher-dimensional gauge theories by decomposing them into layered four-dimensional lattices, proposing a pathway to achieve continuum limits through phase diagram analysis.

Contribution

It introduces a new framework for realizing higher-dimensional theories on lattices by conceptualizing them as multi-layered four-dimensional systems with inter-layer interactions.

Findings

Decomposition of higher-dimensional lattices into layered four-dimensional lattices.

Proposal of a phase diagram-based method to attain continuum limits.

Insight into the behavior of gauge theories in higher dimensions.

Abstract

A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram.